Abstract: A honing machine for finishing a trochoidal bore of a rotor housing of a rotary engine. The honing machine includes a honing head and a machine table both of which are driven by a common drive shaft separately from each other in the same direction but with an eccentricity from each other. The eccentricity is adjustable so as to make the honing head follow smoothly and finely the trochoidal inner surface. A clearance control device is also provided in the honing machine, which controls the clearance between the gears intermeshing with each other for transmitting rotation from the drive shaft to the honing head and machine table. A bias pressure control mechanism is also provided which can control the bias pressure of the honing elements of the head against the trochoidal inner periphery in response to the angular positions of the elements relative to the inner periphery.